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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 3 (1971), S. 47-68 
    ISSN: 1572-9613
    Keywords: Kinetic theory ; nonequilibrium statistical mechanics ; Fokker-Planck and Rice-Allnatt equations ; existence theory for Chapman-Enskog solutions to kinetic equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The linear operators appearing in the Chapman-Enskog solutions to Kirkwood's Fokker-Planck kinetic equation and to Rice and Allnatt's kinetic equation are studied in this article. Existence proofs are given for the linearized Chapman-Enskog equations involving either the Fokker-Planck or the Rice-Allnatt operators. It is shown that the Fokker-Planck and Rice-Allnatt operators, defined in the domain appropriate to kinetic theory, are essentially self-adjoint. It is also shown that the spectrum of either of these operators coincides with the spectrum of the self-adjoint extension of the corresponding operator.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 7 (1973), S. 225-241 
    ISSN: 1572-9613
    Keywords: Kinetic theory ; transport properties of dense fluid
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new kinetic equation is developed which incorporates the desirable features of the Enskog, the Rice-Allnatt, and the Prigogine-Nicolis-Misguich kinetic theories of dense fluids. Advantages of the present theory over the latter three theories are (1) it yields the correct local equilibrium hydrodynamic equations, (2) unlike the Rice-Allnatt theory, it determines the singlet and doublet distribution functions from the same equation, and (3) unlike the Prigogine-Nicolis-Misguich theory, it predicts the kinetic and kinetic-potential transport coefficients. The kinetic equation is solved by the Chapman-Enskog method and the coefficients of shear viscosity, bulk viscosity, thermal conductivity, and self-diffusion are obtained. The predicted bulk viscosity and thermal conductivity coefficients are singular at the critical point, while the shear viscosity and self-diffusion coefficients are not.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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